2.3. Exercises

EXERCISE 2.15.

Calculate and plot the spectrum of a periodic rectangular pulse of period N = 16, if:

images

Note the values of spectral components c0 and cN/2, and show that cNk = c*k for k = 0.15.

EXERCISE 2.16.

Verify the linearity property of the DTFT1D:

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using the following signals:

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with a1 = 1 and a2 = 0.5.

EXERCISE 2.17.

Generate and plot the following signals:

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Verify that the imaginary part of the DTFT of signal x1 [n] is zero; do the same for the real part of the DTFT of signal x2[n].

EXERCISE 2.18.

Show that the DTFT1D is the same for the two discrete-time signals defined below:

images

EXERCISE 2.19.

Write a MATLAB code to verify Parseval's theorem:

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for the signal:

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EXERCISE 2.20.

Write a MATLAB code to verify that the following exponential signal family:

a) contains only ...

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